Locality conjecture for perfectoid algebras

Let $K$ be a perfectoid field, let $(A,A^+)$ be a complete affinoid $K$-algebra, and set $X=\operatorname{Spa}(A,A^+)$. Assume that $X$ has a cover by rational subsets $U_i\subset X$ such that $\mathcal{O}_X(U_i)$ is a perfectoid $K$-algebra. Locality conjecture for perfectoid algebras. Then $A$ is a perfectoid $K$-algebra. A positive answer would make the property of being perfectoid local and simplify foundational arguments; the question is presented as open.